Physical Electronics Slides of Chapter 8 (All Slides)blogs.cae.tntech.edu/bwabegaz42/files/2013/10/Physical-Electronics... · Tennessee Technological University Wednesday, October

Wednesday, October 23, 2013Tennessee Technological University 1

PHYSICAL ELECTRONICS(ECE3540)CHAPTER 8 –THE PN JUNCTION DIODECHAPTER 8 –THE PN JUNCTION DIODE

The PN Junction Diode Chapter 4: we considered the semiconductor in

equilibrium and determined electron and holeconcentrations in the conduction and valencebands, respectively.

The net flow of the electrons and holes in asemiconductor generates current. The process bywhich these charged particles move is calledtransport.

Chapter 5: we considered the two basic transportmechanisms in a semiconductor crystal: drift: themovement of charge due to electric fields, anddiffusion: the flow of charge due to density gradients.


The PN Junction Diode Chapter 6: we discussed the behavior of non-

equilibrium electron and hole concentrations asfunctions of time and space.

We developed the ambi-polar transport equationwhich describes the behavior of the excess electronsand holes.

Chapter 7: We considered the situation in which ap-type and an n-type semiconductor are brought intocontact with one another to form a PN junction.


The PN Junction Diode Previous Chapters: we have been

considering the properties of the semiconductormaterial by calculating electron and holeconcentrations in thermal equilibrium anddetermined the position of the Fermi level.

Previous Chapter: We considered the non-equilibrium condition in which excess electrons andholes are present in the semiconductor.

We discussed the electrostatics of the PN junction inthermal equilibrium and under reverse bias.

We determined the built-in potential barrier in thermalequilibrium and calculated the electric field in thespace charge region. We also considered the junctioncapacitance.


The PN Junction Diode Chapter 8: We will consider the PN junction with a

forward-bias voltage applied and will determine thecurrent-voltage characteristics. The potential barrier ofthe PN junction is lowered when a forward biasvoltage is applied, allowing electrons and holes to flowacross the space charge region.

When holes flow from the p region across the spacecharge region into the n region, they become excessminority carrier holes and are subject to excessminority carrier diffusion, drift, and recombination.

Likewise, when electrons from the n region flowacross the space charge region into the p region, theybecome excess minority carrier electrons and aresubject to these same processes.


The PN Junction Diode When a sufficiently large reverse-bias voltage is applied

across a PN junction, breakdown can occur, producing alarge reverse-bias current in the junction, which can causeheating effects and catastrophic failure of the diode.

Zener diodes, however, are designed to operate in thebreakdown region. Breakdown puts limits on the amountof voltage that can be applied across a PN junction.

When a forward-bias voltage is applied to a PN junction,a current will be induced in the device. We initiallyconsider a qualitative discussion of how charges flow inthe PN junction and then consider the mathematicalderivation of the current-voltage relationship.


Reverse and Forward Applied Bias


Fig. 8.1: Energy band diagram of a PN Junction under reverse and forward bias

Qualitative Description of Charge Flow in a PN Junction

We can qualitatively understand the mechanism of the current in aPN Junction by considering the energy band diagrams. In the lastchapter, we argued that the potential barrier seen by the electronsholds back the large concentration of electrons/holes in the n/pregion and keeps them from flowing into the p/n region. Thepotential barrier, then, maintains thermal equilibrium.

The potential of the n region is positive with respect to the pregion so the Fermi energy in the n region is lower than that in thep region. The total potential barrier is now larger than for the zero-bias case. We argued in the last chapter that the increased potentialbarrier continues to hold back the electrons and holes so that thereis still essentially no charge flow and hence essentially no current.


Qualitative Description of Charge Flow in a PN Junction

When a positive voltage is applied to the p region with respect tothe n region, the Fermi level in the p region is lowered than that inthe n region. The total potential barrier is now reduced. Thesmaller potential barrier means that the electric field in thedepletion region is also reduced.

The smaller electric field means that the electrons and holes are nolonger held back in the n and p regions, respectively. There will bea diffusion of holes from the p region across the space-chargeregion where they now will flow into the n region. Similarly, therewill be a diffusion of electrons from the n region across the space-charge region where they will flow into the p region. The flow ofcharge generates current through the PN junction.


The PN Junction Current The injection of holes into the n region means that these

holes are minority carriers. Likewise, the injection ofelectrons into the p-region means that these electrons areminority carriers.

The behavior of these minority carriers is described bythe ambi-polar transport equations that were discussed inChapter 6. There will be diffusion as well asrecombination of excess carriers in these regions. Thediffusion of carriers implies that there will be diffusioncurrents.

The mathematical derivation of the PN junction current-voltage relationship is considered in the next slides.


Ideal Current-Voltage Relationships The ideal current-voltage relationship of a PN junction is derived

based on four assumptions. The abrupt depletion layerapproximation applies. The space charge regions have abruptboundaries and the semiconductor is neutral outside of thedepletion region.

1. The Maxwell-Boltzmann approximation applies to carrier statistics.2. The concept of low injection applies.3. The concept of total and individual currents:

a) The total current is a constant throughout the entire PNstructure.

b) The individual electron and hole currents are continuousfunctions through the PN structure.

c) The individual electron and hole currents are constantthroughout the depletion region.


Boundary Conditions Considering the conduction-band energy through the PN junction in thermal

equilibrium, the region contains many more electrons in the conduction bandthan the p region; the built-in potential barrier prevents this large density ofelectrons from flowing into the p region. The built-in potential barrier maintainsequilibrium between the carrier distributions on either side of the junction.

An expression for the built-in potential barrier was derived in the last chapterand was given as:

If we divide the equation by Vt = kT/e, take the exponential of both sides, andthen take the reciprocal, we obtain (assuming complete ionization):

where nn0 is the thermal-equilibrium concentration of majority carrier electronsin the n region.


22 lnln||||

i

dat

i

daFpFnbi n

NNVn

NNe

kTV

kTeV

NNn bi

da

i exp2

dn Nn 0

Boundary Conditions In the p region, we can write:

where np0 is the thermal-equilibrium concentration of minority carrier electrons.Substitution yields:

This equation relates the minority carrier electron concentration on the p sideof the junction to the majority carrier electron concentration on the n side ofthe junction in thermal equilibrium.

If a positive voltage is applied to the p region with respect to the n region, thepotential barrier is reduced.

The electric field in the bulk p and n regions is normally very small. Essentiallyall of the applied voltage is across the junction region. The electric field Eappinduced by the applied voltage is in the opposite direction to the thermalequilibrium space charge electric field, so the net electric field in the spacecharge region is reduced below the equilibrium value.


a

ip N

nn2

0

kTeVnn bi

np exp00

The PN Junction Current Under applied potential, the electric field force that prevented majority carriers

from crossing the space charge region is reduced; majority carrier electrons/holesfrom the n/p side are injected across the depletion region into the p/n material.

As long as the bias Va is applied, the injection of carriers across the space chargeregion continues and a current is created in the PN junction. This bias conditionis known as forward bias.

The potential barrier Vbi can be replaced by (Vbi -Va) when the junction is forwardbiased.

If we assume low injection, the majority carrier electron concentration nn0 doesnot change significantly. However, the minority carrier concentration np candeviate from its thermal-equilibrium value np0 by orders of magnitude.


kTeV

kTeVn

kTVVenn abi

nabi

np expexp)(exp 00

kTeVnn a

pp exp0

kTeVnn bi

np exp00

The PN Junction Current When a forward-bias voltage is applied to the PN junction, the junction is no

longer in thermal equilibrium. The total minority carrier electron concentrationin the p region is now greater than the thermal equilibrium value. The forward-bias voltage lowers the potential barrier so that majority carrier electrons fromthe n region are injected across the junction into the p region, thereby increasingthe minority carrier electron concentration. We have produced excess minoritycarrier electrons in the p region.

When the electrons/holes are injected into the p/n region, these excess carriersare subject to the diffusion and recombination processes. We can write that:

where pn0 is the concentration of minority carrier holes at the edge of the spacecharge region in the n region.

By applying a forward-bias voltage, we create excess minority carriers in eachregion of the PN junction.


kTeVpp a

nn exp0

kTeVpp bi

pn exp00

Exercise1. Consider a Silicon PN junction at T = 300 K

so that ni = 1.5 x 1010 cm-3. Assume the n-typedoping is 1 x 1016 cm-3 and assume that aforward bias of 0.60 V is applied to the PNJunction. Calculate the minority carrier holeconcentration at the edge of the space chargeregion for the forward bias that is applied.


kTeVpp a

nn exp0

Solution1. From the equation:

The thermal-equilibrium minority carrier hole concentration is

We then have

Comment: The minority carrier concentration can increase bymany orders of magnitude when a forward bias voltage isapplied. Low injection still applies; however, since the excess-electron concentration (equal to the excess-hole concentrationin order to maintain charge neutrality) is much less than thethermal-equilibrium electron concentration.


3416

222

0 1025.210

)105.1( cmxxNnp

d

in

3144 1059.20259.0

60.0exp1025.2

cmxxp n

kTeVpp a

nn exp0

The PN Junction Current The minority carrier concentrations at the space charge

edges were derived assuming a forward-bias voltage (Va>0)was applied across the pn junction. However, same analysiscould be applied for Va being negative (reverse bias).

If a reverse-bias voltage greater than a few tenths of a voltis applied to the PN junction, then we see from that theminority carrier concentrations at the space charge edgeare essentially zero.

The minority carrier concentrations for the reverse-biascondition drop below the thermal equilibrium values.


Minority Carrier Distribution The ambi-polar transport equation for excess minority carrier holes in an n region

is:

where pn = pn – pn0 is the excess minority carrier hole concentration and is thedifference between the total and thermal equilibrium minority carrierconcentrations.

As a first approximation, we will assume that the electric field is zero in both theneutral p and n regions. In the n region for x > xn we have that E = 0 and g' = 0.If we also assume steady state so (pn)/ (t) = 0, then:

For the same set of conditions, the excess minority carrier electron concentrationin the p region is determined from:


tppg

xpE

xpD n

p

nnp

np

)()()(

0

'2

2

)(:0)(22

2

np

nn xxLp

xp

0

2ppp DL

)(:0)(

22

2

pn

pp xxLn

xn

0

2nnn DL

Minority Carrier Distribution The boundary conditions for the total minority carrier

concentrations are:


kTeVpxp a

nnn exp)( 0

kTeVnxn a

ppp exp)( 0

0)( nn pxp

0)( pp nxn

Minority Carrier Distribution As minority carriers diffuse from the space charge edge into the neutral

semiconductor regions, they will recombine with majority carriers. The excessminority carrier concentrations must approach zero at distances far from thespace charge region. The structure is referred to as a long PN junction.

The general solution is:

Applying the boundary conditions, the coefficients A and D must be zero. Thecoefficients B and C may be determined from the boundary conditions. Theexcess carrier concentrations are then found to be:


)(:)()( 0 nL

xL

x

nnn xxBeAepxpxp pp

)(:)()( 0 pL

xL

x

ppp xxDeCenxnxn nn

)exp(]1)[exp()()( 00p

nannnn L

xxkTeVppxpxp

)exp(]1)[exp()()( 00n

papppp L

xxkTeVnnxnxn

Minority Carrier Distribution The minority carrier concentrations decay exponentially with

distance away from the junction to their thermal-equilibriumvalues. Again, we have assumed that both the n-region and the p-region lengths are long compared to the minority carrier diffusionlengths.

To review, a forward-bias voltage lowers the built-in potentialbarrier of a PN junction so that electrons from the n region areinjected across the space charge region, creating excess minoritycarriers in the p region. These excess electrons begin diffusing intothe bulk p region where they can recombine with majority carrierholes.

The excess minority carrier electron concentration then decreaseswith distance from the junction. The same discussion applies toholes injected across the space charge region into the n region.


Ideal PN Junction Current The total current in the junction is the sum of the individual electron and

hole currents which are constant through the depletion region. Since the electron and hole currents are continuous functions through

the PN junction, the total PN junction current will be the minority carrier hole diffusion current at x = xn plus the minority carrier electron diffusion current at x = -xp.

The gradients in the minority carrier concentrations produce diffusion currents, and since we are assuming the electric field to be zero at the space charge edges, we can neglect any minority carrier drift current component.

We can calculate the minority carrier hole diffusion current density as: (assuming uniformly doped regions)


nxxn

pnp dxxpdeDxJ |))(()(

nxxn

pnp dxxdpeDxJ |)()(

Ideal PN Junction Current Taking the derivative and substituting: :

The hole current density for this forward-bias condition is in the +x direction, which is from the p to the n region.

Similarly, we may calculate the electron diffusion current density at x=-xp. This may be written as:

Using Equation (8.15). we obtain:

The electron current density is also in the +x direction. An assumption we made at the beginning was that the individual electron

and hole currents were continuous functions and constant through the space charge region. The total current is the sum of the electron and hole currents and is constant through the entire junction.


]1)[exp()( 0 kTeV

LpeD

xJ a

p

npnp

pxxp

npn dxxnd

eDxJ |))((

)(

]1)[exp()( 0 kTeV

LneD

xJ a

n

pnpn

Ideal PN Junction Current The total current density in the PN junction is then:

Parameter Js is defined as:

Substituting Js, the ideal diode equation may be written as:


]1)[exp()()( 00

kTeV

LneD

LpeD

xJxJJ a

n

pn

p

nppnnp

n

pn

p

nps L

neDL

peDJ 00

]1)[exp()()( kTeVJxJxJJ a

spnnp

Ideal PN Junction Current

The above equation, known as the ideal-diode equation, gives agood description of the current-voltage characteristics of the PNjunction over a wide range of currents and voltages. Although theequation was derived assuming a forward-bias voltage, there isnothing to prevent Va from being negative (reverse bias).

If the voltage Va becomes negative (reverse bias) by a few kT/e V,then the reverse-bias current density becomes independent of thereverse-bias voltage. The parameter Js is then referred to as thereverse saturation current density. The current-voltagecharacteristics of the PN junction diode are obviously not bilateral.


]1)[exp()()( kTeVJxJxJJ a

spnnp

Reverse and Forward Applied Bias


Fig. 8.2: Ideal I-V Characteristic of a PN Junction Diode

Exercise2. Consider the following parameters in a Silicon

PN Junction: Na = Nd = 1016cm-3 ni = 1.5 x 1010 cm-3

Dn= 25 cm2/s p0= n0 = 5 x10-7 s Dp = 10 cm2/s r = 11.7

Determine the ideal reverse saturation currentdensity in the Silicon PN junction at T = 100 K.


Solution2. The ideal reverse saturation current density is given by

which may be rewritten as:

Substituting the parameters, we obtain Js = 4.15x10-11A/cm2

Comment The ideal reverse-bias saturation current density is very

small. If the PN Junction cross-sectional area were A =10-4 cm2, for example, then the ideal reverse-bias diodecurrent would be Is = 4.15 x 10-15 A.


n

pn

p

nps L

neDL

peDJ 00

00

2 11

p

d

dn

n

ais

DN

DN

enJ

Total Forward Bias Current The total forward-bias current density in the PN junction is the

sum of the recombination and the ideal diffusion current densities.

The diode current-voltage relationship can be written as:

where n is called the ideality factor and 1<n<2. For a large forward-bias voltage, n=1 when diffusion dominates and for lowforward-bias, n=2 when recombination dominates.


]1)[exp( nkTeVII a

s

Drec JJJ

kTeVJ

kTeVeWnJ a

rai

rec 2exp

2exp

2 00

kTeVJJ a

sD exp

Reading Assignment Please read the concepts of Junction Breakdown and the

operation principles of Zener Diodes from your textbook (last pages of Chapter 8).

In class, we have started explaining these concepts. After the reading assignment, we will go through the

concepts of a large reverse-bias voltage that causes aJunction Breakdown.

We will also discuss the Zener Effect and the AvalancheEffect.


Picture Credits Semiconductor Physics and Devices, Donald Neaman, 4th

Edition, McGraw Hill Publications. B. Van Zeghbroeck, Principles of Electronic Devices,

Department of ECE, University of Colorado,Boulder, 2011.http://ecee.colorado.edu/~bart/book/book/contents.htm

Animation of the PN Junction formation, Universityof Cambridge, 2013.http://www.doitpoms.ac.uk/tlplib/semiconductors/pn.php

W. U. Boeglin, PN Junction, Florida InternationalUniversity, 2011.http://wanda.fiu.edu/teaching/courses/Modern_lab_manual/pn_junction.html


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Physical Electronics Slides of Chapter 8 (All Slides)blogs.cae.tntech.edu/bwabegaz42/files/2013/10/Physical-Electronics... · Tennessee Technological University Wednesday, October